WASHINGTON — After weeks of ultimatums, President Barack Obama and congressional Republicans are exploring whether they can end a budget standoff that has triggered a partial government shutdown and edged Washington to the verge of a historic, economy-jarring federal default.

The two sides planned to continue discussions today, a day after Obama and top administration officials met for 90 minutes with House Speaker John Boehner and other House GOP leaders at the White House. No agreement was reported and plenty of hurdles remained, but both sides cast their meeting positively as, for the first time, hopes emerged that a resolution might be attainable, even if only a temporary one.

Obama planned a late-morning White House meeting with GOP senators, who said they would present options of their own for ending the shutdown and debt limit standoff. Determined to resolve the twin crises, the Republicans have reached out to senior Democrats, including New York Sen. Chuck Schumer.

A White House statement about Thursday’s meeting with House Republicans said “no specific determination was made” but added, “The president looks forward to making continued progress with members on both sides of the aisle.”

House Majority Leader Eric Cantor, R-Va., said the meeting was “clarifying for both sides” and that following a night of negotiations, “hopefully we can see a way forward.”

The talks were held shortly before a Wall Street Journal/NBC News poll was released bearing ominous news for the GOP. It showed more people blaming Republicans than Obama for the shutdown, 53 percent to 31 percent. Just 24 percent viewed the GOP positively, compared with 39 percent with positive views of the Democratic Party.

Boehner, R-Ohio, brought a proposal to the White House meeting to extend federal borrowing authority through Nov. 22, conditioned on Obama’s agreeing to negotiate over spending cuts and the government shutdown. But participants said the discussion expanded to ways to quickly end the shutdown, which entered its 11th day today.

“It’s clear he’d like to have the shutdown stopped,” House Appropriations Committee Chairman Hal Rogers, R-Ky., said of Obama. “And we’re trying to find out what he would insist upon” to reopen the government “and what we would insist upon.”

One major problem for Boehner’s plan was highlighted by Senate Majority Leader Harry Reid, D-Nev. After he and fellow Senate Democrats had their own White House meeting with Obama, Reid said negotiations before the government reopens — a key part of Boehner’s proposal — were “not going to happen.”